Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 60, Number 3 (2019), 333-351.
Residue Field Domination in Real Closed Valued Fields
We define a notion of residue field domination for valued fields which generalizes stable domination in algebraically closed valued fields. We prove that a real closed valued field is dominated by the sorts internal to the residue field, over the value group, both in the pure field and in the geometric sorts. These results characterize forking and þ-forking in real closed valued fields (and also algebraically closed valued fields). We lay some groundwork for extending these results to a power-bounded -convex theory.
Notre Dame J. Formal Logic, Volume 60, Number 3 (2019), 333-351.
Received: 21 February 2017
Accepted: 17 October 2017
First available in Project Euclid: 2 July 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03C64: Model theory of ordered structures; o-minimality
Secondary: 03C60: Model-theoretic algebra [See also 08C10, 12Lxx, 13L05] 12J10: Valued fields 12J25: Non-Archimedean valued fields [See also 30G06, 32P05, 46S10, 47S10]
Ealy, Clifton; Haskell, Deirdre; Maříková, Jana. Residue Field Domination in Real Closed Valued Fields. Notre Dame J. Formal Logic 60 (2019), no. 3, 333--351. doi:10.1215/00294527-2019-0015. https://projecteuclid.org/euclid.ndjfl/1562033115